In recent years, information communication techniques more widely have been implemented in the form of, for example, electronic commerce and electronic mails. To cope with this, cryptographic techniques in information transmission have been also researched and developed. As one of the cryptographic techniques, quantum cryptography is highly expected recently.
In the quantum cryptography, security is ensured by utilizing a physical phenomenon according to Heisenberg's uncertainty principle in quantum mechanics. According to the uncertainty principle, a quantum state is changed by observation, and therefore, eavesdropping (observation) of a communication cannot be performed without being surely detected. This allows taking measures against the eavesdropping, such as blocking the communication. This makes eavesdropping physically impossible in the quantum cryptography. Further, according to the uncertainty principle, replication of particles is also impossible in the quantum cryptography.
Quantum teleportation is an important feature in the quantum cryptography. The quantum teleportation is a technique for transmitting only quantum information of the particles to another place. The quantum teleportation is realized by exchanging information between photons by utilizing a quantum-entangled state. A photon pair in the quantum-entangled state has such a property that a quantum state of one of the photons is determined when a quantum state of the other one of the photons is determined. This property is not dependent on a distance between the two photons.
In the quantum teleportation technique, such photon pairs in the quantum-entangled state are essential.
The following describes a two-photon polarization-entangled state. It is known that a quantum-entangled state of 2 quantum bits (two photons) using polarized light takes the following 4 states.
      Math    .                  ⁢    1                                                                                                                                                                                                                                                                                                                                                                                              |                                                                              Ψ                                        ±                                                                                                              〉                                                                    12                                                                ≡                                                                                                      1                                                                          2                                                                                                        ⁢                                                                                                            (                                                                              |                                        H                                                                            〉                                                                        1                                                                                                                              |                              V                                                        〉                                                    2                                                ±                                            |                      V                                        〉                                    1                                |                H                            〉                        2                    )                                      (          1          )                                                                                                                                                                                                                                                                                                                                                                                                            |                                                                              Φ                                        ±                                                                                                              〉                                                                    12                                                                ≡                                                                                                      1                                                                          2                                                                                                        ⁢                                                                                                            (                                                                              |                                        H                                                                            〉                                                                        1                                                                                                                              |                              H                                                        〉                                                    2                                                ±                                            |                      V                                        〉                                    1                                |                V                            〉                        2                    )                                      (          2          )                    
A light path of the photon and an angular frequency of the photon are some of physical quantities to determine a mode i of a photon.
The following describes a method (parametric down-conversion) for producing two photons. As a physical process to produce a two-photon state, a parametric down-conversion process is often used. In the parametric down-conversion process, a single pump photon (angular frequency ωp, wave vector kp) incident on a crystal is converted into a photon pair with a certain probability. One of the photon pair is a signal photon (angular frequency ωs, wave vector ks) and, the other one of the photon pair is an idler photon (angular frequency ωi, wave vector ki). At this time, in order that the parametric down-conversion process may be caused, the following phase matching condition should be satisfied.
Math. 2ωp=ωs+ωi  (3)kp=ks+ki  (4)
There are 3 types of the phase matching conditions depending on polarization of the photons.    1. Type-O Phase Matching Condition    This is a case where the pump photon, the signal photon, and the idler photon have the same polarization.    2. Type-I Phase Matching Condition    This is a case where the signal photon and the idler photon have the same polarization, and the polarization of the pump photon is perpendicular to the polarization of the signal photon and the idler photon.    3. Type-II Phase Matching Condition    This is a case where the polarization of the signal photon is perpendicular to the polarization of the idler photon, and the pump photon has the same polarization as either of the polarization of the signal photon and the polarization of the idler photon.
Next will be explained a quasi phase matching method. The quasi phase matching method is well known as a technique for satisfying the phase matching condition at a certain wavelength. In the quasi phase matching method, a second order nonlinear optical susceptibility is periodically modulated so as to satisfy the phase matching condition. In this case, the above expression (4) of the phase matching condition is changed to the following expression (5):
      Math    .                  ⁢    3                                            k            p                    =                                    k              s                        +                          k              i                        +                                          2                ⁢                π                            Λ                                                            (          5          )                    where Λ is a modulation period of the second order nonlinear optical susceptibility. A “periodic polarization reversal method” in which spontaneous polarization of a crystal is periodically reversed is put into practice as a technique for periodically modulating the second order nonlinear optical susceptibility.
The following describes a conventional method for producing a polarization-entangled state. There have been reported several techniques as the method for producing a polarization-entangled state in which two photons have the same angular frequency (for example, see Non Patent Literature 1). In this method, since the two photons have the same angular frequency and therefore it is difficult to distinguish them from each other, a mode is determined according to a light path of the photon. That is, the two photons should be emitted in different light paths.
Further, there has been also suggested a method for producing a polarization-entangled state in which two photons have different angular frequencies. In this method, since the photons are distinguished from each other according to the angular frequencies, the two photons may be emitted in the same light path.
As the method for producing a polarization-entangled photon pair constituted by two photons having different angular frequencies, there have been reported the following methods.
1. A Method Utilizing a Parametric Down-Conversion of Type-O or Type-I (Non Patent Literature 2)    This method utilizes nonlinear optical crystals that satisfy the phase matching conditions type-O or type-I so as to generate two photons having the same polarization state. The nonlinear optical crystals are aligned in series by being rotated in opposite directions by 90 degrees. In this case, the two crystals are irradiated by light from the same pump light source, so as to generate two photons (ω1, ω2) having different angular frequencies in a coaxial direction of pump light.
2. A Method for Producing Two Types of Periodically Poled Structures in a Single Crystal (Patent Literature 2)    This method employs different phase matching conditions type-O and type-I.
3. A Method Utilizing a Four-Wave Mixing Process that is a Third Nonlinear Optical Phenomenon Caused in Optical Fibers (Non Patent Literature 3)    In this method, optical fibers are set in an interferometer and a polarization-entangled state is generated.
Further, a method in which non-degenerate polarization-entangled photon pairs are produced by utilizing a two-photon resonance excitation process in a semiconductor has been also known (Patent Literature 1).
Citation List
Patent Literature 1
Japanese Patent Application Publication, Tokukai, No. 2005-309012 A (Publication Date: Nov. 4, 2005)
Patent Literature 2
Japanese Patent Application Publication, Tokukai, No. 2007-114464 A (Publication Date: May 10, 2007)
Non Patent Literature 1
“New high-intensity source of polarization-entangled photon pairs.” P. G. Kwiat et al., Phys. Rev. Lett. 75, 4337 (1995).
Non Patent Literature 2
“Bright, single-spatial-mode source of frequency non-degenerate, polarization-entangled photon pairs using periodically poled KTP.” M. Pelton et al., Opt. Express 12, 3573 (2004).
Non Patent Literature 3
“Generation of polarization-entangled photon pairs and violation of Bell's inequality using spontaneous four-wave mixing in a fiber loop,” H. Takesue and Kyo Inoue, Phys. Rev. A 70, 031802 (2004).